Solve the following Linear Programming Problem via the Simplex Method:?

Help!! I need to know what the inequalities/equations are to set up this problem:

Solve the following Linear Programming Problem via the Simplex Method:

A city council is working with a hotel developer to build several hotels along its beach-front.

The developer has three prototypes: a convention-style hotel with 500 rooms costing $100 million, a vacation-style hotel with 200 rooms costing $20 million, and a small hotel with 50 rooms costing $4 million.

The city council wants a total capacity of at least 3,000 rooms and has three other restrictions:

• at most three convention-style hotels;

• at most twice as many small hotels as vacation-style; and

• at least a fifth as many convention-style hotels as vacation-style and small combined.

How many hotels of each type should the council request in order to minimize cost?

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  • 7 years ago
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    Big Hi!

    Solve the following Linear Programming Problem via the Simplex Method:?

    Help!! I need to know what the inequalities/equations are to set up this problem:

    Solve the following Linear Programming Problem via the Simplex Method:

    A city council is working with a hotel developer to build several hotels along its beach-front.

    The developer has three prototypes: a convention-style hotel with 500 rooms costing $100 million, a vacation-style hotel with 200 rooms costing $20 million, and a small hotel with 50 rooms costing $4 million.

    The city council wants a total capacity of at least 3,000 rooms and has three other restrictions:

    • at most three convention-style hotels;

    • at most twice as many small hotels as vacation-style; and

    • at least a fifth as many convention-style hotels as vacation-style and small combined.

    How many hotels of each type should the council request in order to minimize cost?

    Let C = Convention-style Hotel → 500 rm costing $ 100 Million

    V = vacation-style hotel → 200 rm $ 20 million

    S = small hotel → 50 $ 4 million

    CONDITIONS:

    1. Capacity = 3,000 rooms

    2. C ≤ 3

    3. S = 2V

    4. C = 1/5 (V + S)

    C + V + S = 3000 ← eq5

    C = 3 ◄ No. of Convention Hotels

    From 4

    C = 1/5 (V + S)

    3 = 1/5 (V + 2V)

    15 = 3V

    ==================================

    V = 5 ◄ No. of Vacation-style Hotels

    ==================================

    Substitute V to 3

    S = 2(5)

    ==============================

    S = 10 ◄ No. of Small Hotels

    ==============================

    From eq5

    C + V + S = 3000

    3(500) + 5(200) + 10(50) = 3000

    1500 + 1000 + 500 = 3000

    3000 = 3000 ← Correct

    Cost

    C = 3 (100 m ) → $ 300 m

    V = 5 (20 m ) → $ 100 m

    S = 10 (4 m ) → $ 40 m

    ==========================

    Total → $ 440 million

    ==========================

    Hope this helps

    Remember that Jesus loves you. Know Him in His words the Bible.

    God Bless

    Lim♥E

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